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A prime number (or prime) is a ... 181–200 1087: 1091: 1093: 1097: 1103: ... A cluster prime is a prime p such that every even natural number k ≤ p − 3 is the ...
A number where some but not all prime factors have multiplicity above 1 is neither square-free nor squareful. The Liouville function λ(n) is 1 if Ω(n) is even, and is -1 if Ω(n) is odd. The Möbius function μ(n) is 0 if n is not square-free. Otherwise μ(n) is 1 if Ω(n) is even, and is −1 if Ω(n) is odd.
Mersenne primes and perfect numbers are two deeply interlinked types of natural numbers in number theory. Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2 p − 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1.
These numbers have been proved prime by computer with a primality test for their form, ... 200 17×2 8636199 + 1 [71] 17 February 2021 2,599,757 201 75898 524288 + 1
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Plot of the number of divisors of integers from 1 to 1000. Highly composite numbers are in bold and superior highly composite numbers are starred. ... 200 1 deficient ...
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For example, eight of the first 11 primes p give rise to a Mersenne prime M p (the correct terms on Mersenne's original list), while M p is prime for only 43 of the first two million prime numbers (up to 32,452,843). Since Mersenne numbers grow very rapidly, the search for Mersenne primes is a difficult task, even though there is a simple ...